Answered

IDNLearn.com connects you with experts who provide accurate and reliable answers. Find the answers you need quickly and accurately with help from our knowledgeable and dedicated community members.

The table shows the growth, in centimeters, of plants in two different soils after two weeks.

Soil Type vs. Plant Growth

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Soil A & 3.1 & 5.2 & 4.6 & 3.8 & 6.0 & 4.3 & 3.7 & 4.0 & 3.5 & 3.5 \\
\hline
Soil B & 2.9 & 3.8 & 5.0 & 4.8 & 4.5 & 3.9 & 3.9 & 4.4 & 5.5 & 4.1 \\
\hline
\end{tabular}

Which statement explains which soil tended to have greater growth?

A. Soil A had greater growth because its data have a greater standard deviation.
B. Soil A had greater growth because its data have a greater mean.
C. Soil B had greater growth because its data have a greater interquartile range.
D. Soil B had greater growth because its data have a greater median.

Sagot :

GinnyAnsweridn
Let's analyze the growth data for plants in soils A and B to determine which soil tended to have greater growth.

First, we calculate the mean growth for each soil type:
- Mean growth for Soil A: [tex]\(4.17\)[/tex] cm
- Mean growth for Soil B: [tex]\(4.28\)[/tex] cm

Next, we calculate the standard deviation for each soil type, which measures the variation or dispersion of the growth data:
- Standard deviation for Soil A: [tex]\(0.8391\)[/tex] cm
- Standard deviation for Soil B: [tex]\(0.6925\)[/tex] cm

We also calculate the median growth for each soil type, which is the middle value when the data points are ordered:
- Median growth for Soil A: [tex]\(3.9\)[/tex] cm
- Median growth for Soil B: [tex]\(4.25\)[/tex] cm

Finally, we calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile, providing a measure of statistical dispersion:
- IQR for Soil A: [tex]\(0.975\)[/tex] cm
- IQR for Soil B: [tex]\(0.825\)[/tex] cm

Now, we assess the given statements:

1. "Soil A had greater growth because its data have a greater standard deviation."
- This statement is not accurate since standard deviation alone does not determine greater growth; it only indicates variability in the data.

2. "Soil A had greater growth because its data have a greater mean."
- This statement is incorrect because the mean growth for Soil A ([tex]\(4.17\)[/tex] cm) is actually less than that for Soil B ([tex]\(4.28\)[/tex] cm).

3. "Soil B had greater growth because its data have a greater interquartile range."
- This statement is incorrect because Soil B has a smaller IQR ([tex]\(0.825\)[/tex] cm) compared to Soil A ([tex]\(0.975\)[/tex] cm).

4. "Soil B had greater growth because its data have a greater median."
- This statement is correct because the median growth for Soil B ([tex]\(4.25\)[/tex] cm) is greater than the median growth for Soil A ([tex]\(3.9\)[/tex] cm).

Therefore, the correct statement is:
Soil B had greater growth because its data have a greater median.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.